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FIZIKA A 15 (2006) 2 , 91-112
 
INTRODUCING NONLINEAR TIME SERIES ANALYSIS IN UNDERGRADUATE COURSES
MATJAŽ PERC
Department of Physics, Faculty of Education, University of Maribor,
Koroška cesta 160, SI-2000 Maribor, Slovenia
E-mail address: matjaz.perc@uni-mb.si
Received 25 October 2004; Accepted 12 July 2006
Online 1 December 2006
This article is written for undergraduate students and teachers
who would like to get familiar with basic nonlinear time series
analysis methods. We present a step-by-step study of a simple example
and provide user-friendly programs that allow an easy reproduction
of presented results. In particular, we study an artificial time
series generated by the Lorenz system. The mutual information and
false nearest neighbour method are explained in detail, and used
to obtain the best possible attractor reconstruction. Subsequently,
the times series is tested for stationarity and determinism, which
are both important properties that assure correct interpretation of
invariant quantities that can be extracted from the data set. Finally,
as the most prominent invariant quantity that allows distinguishing
between regular and chaotic behaviour, we calculate the maximal
Lyapunov exponent. By following the above steps, we are able to
convincingly determine that the Lorenz system is chaotic directly
from the generated time series, without the need to use the
differential equations. Throughout the paper, emphasis on clear-cut
guidance and a hands-on approach is given in order to make the
reproduction of presented results possible also for undergraduates,
and thus encourage them to get familiar with the presented theory.
PACS numbers: 01.50.-i, 05.45.Tp
UDC 530.182
Keywords: nonlinear time series analysis, physics education
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